Pseudo – Differential Operators

A Pseudo-differential operator t is defined by means of a symbol (x, y) which is a function of x in Rn and y in IRn (sometimes restricted to y ¹ 0) and by the formal rule  t ( exp( ix . y ) ) = f( x , y ) exp ( ix . y) which is reminiscent of amplitude modulation in radio detection. We showed that the operator  ( - x –1 d / dx ) v , v  e en , is indeed a pseudo differential operator. Some very exciting properties of this operator have been obtained and we are proving it further.

Faculty Involved : Om P. Singh